This is the part I have a problem with:

Gender is a category assigned by the individual

Gender isn't assigned by the individual. Gender is assigned by parents, doctors, the community, and society broadly. Gender is an inherently social construction. Some people have misconstrued this to mean that gender is an individual construction. It is not. How you see yourself is only part what makes you, you. You are also defined by how others see you. I understand that some people don't identify with the gender that has been assigned to them, and thus want to change their gender assignment, and I empathize with those people, but whether or not they are able to do this is at least partially out of their control. Just because you see yourself a certain way, doesn't mean others will see you that way, and, again we are defined not only by how we perceive ourselves, but how others perceive us.

Umm, people can definitely change how others view them. And if person A refuses to accept person B for who they are, that doesn’t define person B. It defines person A as an asshole.

And if person A refuses to accept person B for who they are, that doesn’t define person B. It defines person A as an asshole.

Agree. And that sentence is not only valid for gender, it's for anything other cultural label (like genders are).

If I say that I'm a gamer, or a fan of star wars, or whatever, and you're spending your energy trying to convince the world I'm not what I said... it says much more about you than about me.

that sentence is not only valid for gender, it's for anything other cultural label (like genders are).

How about race? Can white people elect to be Black?

This is a bad faith argument, and at best a whataboutism. They aren't remotely related.
Are you aware of a good rebuttal to the comment you replied to? It tends to trip me up as even through it's often presented in bad faith, our concept of race is mostly cultural too isn't it? It feels like they're different somehow, but I can't articulate the reason why and so it's like I've stumbled into a "gotcha".
gender is a social construct which can change depending on social expectations or the mental feeling of the individual, while race is a biological construct that can't be changed
But what kind of people put so much energy into trying to show person A that it is indeed the case? Person A may be an asshole to refuse the evidence, but person B could also be selfish to take a lot of energy into convincing person A of something that might not be apparent or even might not even reflect reality. It doesn't mean that one is more right than the other or being disrespectful. Truth hurts after all. But then, if someone keep repeating the truth, maybe that person becomes an asshole. Or maybe we should ask this person if it is indeed an asshole to not misslabel them an asshole and hurt its feeling.
Describing misgendering someone as "truth" is simply transphobia. Be better.
That doesn't change much; just means people should place more value in what a person themself identifies with. Some people being inconsiderate doesn't mean others should be too.

Gender isn’t assigned by the individual. Gender is assigned by parents, doctors, the community, and society broadly. Gender is an inherently social construction.

Social/cultural construction doesn't mean that it has to be a collective construction.

Your gender is not different from something like... being a nerd, or being a fan of star wars. Someone might call you a nerd, but ultimately it's up to you to embrace that label or not.

And anyway, cultural things like gender, being a nerd, etc is absolutely unrelated to biology.

Social/cultural construction doesn't mean that it has to be a collective construction.

It absolutely does mean that. We just live in this age of hyper individualism, where people attempt to atomize the individual from the collective, as though the individual is something wholly its own, but it isn't. It's not possible to separate the individual from the collective.

It's not possible to separate the individual from the collective.

What's it like, being from a planet with a hive mind?

You're thinking in the right direction, but you're not quite there. Yes, gender gets assigned at birth as your biological phenotype (because the overwhelming majority of humans identify as cis gender). Humans become individuals and eventually realize that maybe their assigned gender does not fit them. At this point it becomes their own choice and it overrides any gender assignment given at birth. Depending on the individual, gender changes from something that's assigned to something you assign yourself.

Yes, genders are tentatively assigned at birth because most languages are based on gendered pronouns and gendered words. So we need a gender to refer to this new person, and we can't ask babies for their input.

But that's not different than a parent saying his baby will like sports. Or, in my case, saying your baby will grow up to play Magic The Gathering with you.

Because when they're old enough to decide for themselves, they can change whatever temporary labels you attached to them. And they can say they don't like Magic. Gender. I meant gender.

most languages are based on gendered pronouns and gendered words.

Relevant Tom Scott video: https://youtu.be/46ehrFk-gLk

First, only about 25% of languages are fully based around everything being gendered.

Second English has some specifically gendered words as remnants from old English and the languages that blended together to make English.

Third, of those gendered languages, they don't necessarily agree on what gender things are. In the video, they mention that "A Key" in German is masculine and in Spanish is feminine.

First, only about 25% of languages are fully based around everything being gendered.

Guilty of western bias. But should be a bit obvious that I didn't mean smaller languages, or languages spoken from people that are usually not here discussing with us. But if it wasn't obvious before, I am making it explicit now.

Third, of those gendered languages, they don’t necessarily agree on what gender things are. In the video, they mention that “A Key” in German is masculine and in Spanish is feminine.

How different languages gender a key (or a chair, or teapot, or whatever object) is not really relevant for a discussion about genders in people.

And I don't even mean that to defend anything, just trying to explain why people apply genders to babies. And how people just do that for convenience, and how that's not relevant as a "permanent" gender.

At this point it becomes their own choice and it overrides any gender assignment given at birth.

That's not true. Your gender assignment is defined by how others treat you, how they interact with you, and that's not completely under the individual's control. You can't choose how other people view you, at least not entirely.

Well, sometimes people are wrong and you seem to be wrong right now. I think you have some misconceptions about the definition of gender and biological sex.
Unless it’s reasonable for me to address you in business dealings as “smegma John” it seems we might put more emphasis on how someone identifies and wants to be called than what anyone else wants to impose on them

The social construct part of Gender is that the terms were constructed by society - they represented the stereotypes of how different sexes would express themselves. It's in modern times that these are more explicitly detached due to our better understanding of Gender and sex.

People perceive themselves based on their Gender as much as other people do, and it is not necessarily true that a person's perception of themselves (their gender) lines up with their sex - hence Gender dysphoria.

It is one thing to accidentally misgender someone because gender affirmation isn't always outwardly obvious (particularly for non-binary folks), but refusing to make that consideration at all, even when aware of it, would say more about you than it would them.